What do the following two equations represent? $3x-2y = 5$ $3x-2y = -2$
Solution: Putting the first equation in $y = mx + b$ form gives: $3x-2y = 5$ $-2y = -3x+5$ $y = \dfrac{3}{2}x - \dfrac{5}{2}$ Putting the second equation in $y = mx + b$ form gives: $3x-2y = -2$ $-2y = -3x-2$ $y = \dfrac{3}{2}x + 1$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.